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Dietterich, Editor  \nChristopher Bishop, David Heckerman, Michael Jordan, and Michael Kearns, Associate Editors  \nBioinformatics: The Machine Learning Approach, Pierre Baldi and Søren Brunak Reinforcement Learning: An Introduction, Richard S. Sutton and Andrew G. Barto  \nGraphical Models for Machine Learning and Digital Communication, Brendan J. Frey  \nLearning in Graphical Models, Michael I. Jordan  \nCausation, Prediction, and Search, second edition, Peter Spirtes, Clark Glymour, and Richard Scheines  \nPrinciples of Data Mining, David Hand, Heikki Mannilla, and Padhraic Smyth  \nBioinformatics: The Machine Learning Approach, second edition, Pierre Baldi and Søren Brunak  \nLearning Kernel Classifiers: Theory and Algorithms, Ralf Herbrich  \nLearning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond, Bernhard Schölkopf and Alexander J. Smola  \nLearning Kernel Classifiers Theory and Algorithms  \nRalf Herbrich  \nThe MIT Press Cambridge, Massachusetts London, England  \n􀀁c2002 Massachusetts Institute of Technology  \nAll rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher.  \nThis book was set in Times Roman by the author using the LATEX document preparation system and was printed and bound in the United States of America.  \nLibrary of Congress Cataloging-in-Publication Data  \nHerbrich, Ralf.  \nLearning kernel classifiers : theory and algorithms / Ralf Herbrich.  \n[p. cm](p. cm).—(Adaptive computation and machine learning) Includes bibliographical references and index.  \nISBN 0-262-08306-X (hc. : alk. paper)  \n1. Machine learning. 2. Algorithms. I. Title. II. Series.  \nQ325 .5 .H48 2001 006.3􀀂 1 dc21  \n2001044445  \nTo my wife, Jeannette  \nThere are many branches of learning theory that have not yet been analyzed and that are important  \nboth for understanding the phenomenon of learning and for practical applications. They are waiting for their researchers.  \n—Vladimir Vapnik  \nGeometry is illuminating; probability theory is powerful.  \n—Pál Ruján  \nContents  \nSeries Foreword xv  \nPreface xvii  \n1 Introduction 1  \n1.1 The Learning Problem and (Statistical) Inference 1  \n1.1.1 Supervised Learning ............... 3  \n1.1.2 Unsupervised Learning .............. 6  \n1.1.3 Reinforcement Learning ............. 7  \n1.2 Learning Kernel Classifiers 8  \n1.3 The Purposes of Learning Theory 11  \nI LEARNING ALGORITHMS  \n2 Kernel Classifiers from a Machine Learning Perspective 17  \n2.1 The Basic Setting 17  \n2.2 Learning by Risk Minimization 24  \n2.2.1 The (Primal) Perceptron Algorithm ....... 26  \n2.2.2 Regularized Risk Functionals .......... 27  \n2.3 Kernels and Linear Classifiers 30  \n2.3.1 The Kernel Technique .............. 33  \n2.3.2 Kernel Families .................. 36  \n2.3.3 The Representer Theorem ............ 47  \n2.4 Support Vector Classification Learning 49  \n2.4.1 Maximizing the Margin ............. 49  \n2.4.2 Soft Margins—Learning with Training Error .. 53  \n2.4.3 Geometrical Viewpoints on Margin Maximization 56  \n2.4.4 The ν–Trick and Other Variants ......... 58  \nx Contents  \n2.5 Adaptive Margin Machines 61  \n2.5.1 Assessment of Learning Algorithms ....... 61  \n2.5.2 Leave-One-Out Machines ............ 63  \n2.5.3 Pitfalls of Minimizing a Leave-One-Out Bound . 64  \n2.5.4 Adaptive Margin Machines ............ 66  \n2.6 Bibliographical Remarks 68  \n3 Kernel Classifiers from a Bayesian Perspective 73  \n3.1 The Bayesian Framework 73  \n3.1.1 The Power of Conditioning on Data ....... 79  \n3.2 Gaussian Processes 81  \n3.2.1 Bayesian Linear Regression ........... 82  \n3.2.2 From Regression to Classification ........ 87  \n3.3 The Relevance Vector Machine 92  \n3.4 Bayes Point Machines 97  \n3.4.1 Estimating the Bayes Point ............ 100  \n3.5 Fisher Discriminants 103  ","cbCair5HQajwbeJr","https://ap.wps.com/l/cbCair5HQajwbeJr","pdf",2820927,371,"English","# Series Foreword\n# Preface\n# Introduction\n## The Learning Problem and (Statistical) Inference\n## Learning Kernel Classifiers\n## The Purposes of Learning Theory\n# Kernel Classifiers from a Machine Learning Perspective\n## The Basic Setting\n## Learning by Risk Minimization\n## Kernels and Linear Classifiers\n## Support Vector Classification Learning\n## Adaptive Margin Machines\n# Kernel Classifiers from a Bayesian Perspective\n## The Bayesian Framework\n## Gaussian Processes\n## The Relevance Vector Machine\n## Bayes Point Machines\n## Fisher Discriminants\n# Mathematical Models of Learning\n## Generative vs. Discriminative Models\n## PAC and VC Frameworks\n## The Luckiness Framework\n# Bounds for Specific Algorithms\n## The PAC-Bayesian Framework\n## Compression Bounds\n## Algorithmic Stability Bounds\n# Appendices\n## Theoretical Background and Basic Inequalities\n## Proofs and Derivations—Part I","[{\"question\":\"What problem does the book focus on?\",\"answer\":\"The book focuses on learning kernel classifiers and analyzing how learning theory supports understanding and designing kernel-based learning algorithms. It frames learning in terms of inference and risk minimization, then expands to Bayesian modeling and theoretical guarantees.\"},{\"question\":\"How does the book explain kernel classifiers?\",\"answer\":\"It derives kernel classifiers from a machine learning perspective using kernels and linear classifier viewpoints, including the representer theorem and support vector classification. It also presents a Bayesian perspective using models such as Gaussian processes, relevance vector machines, and related Bayesian approaches.\"},{\"question\":\"What kind of theoretical results are included?\",\"answer\":\"The book develops mathematical learning models (including PAC and VC frameworks) and provides bounds for specific algorithms. It includes PAC-Bayesian bounds, compression bounds, and algorithmic stability bounds, with supporting theoretical background in appendices.\"}]","Learning Kernel Classifiers - Theory and Algorithms | PDF",1789974070,935]